Apparatus and method for treating neurological disorders

ABSTRACT

An apparatus for treating neurological disorders comprising at least one electrode implantable in a patient&#39;s brain and a processing and stimulation device connected to the at least one electrode. The processing and stimulation device comprises at least one stimulation module adapted to generate a stimulation signal characterised by a plurality of parameters; at least one acquisition module adapted to acquire a signal characteristic of cerebral activity and determine its power in at least one frequency band; and at least one control module of at least one parameter of the stimulation signal as a function of the power of the signal characteristic of cerebral activity acquired, based on a transfer function having a saturating trend, wherein the transfer function is configured to set the at least one parameter of the stimulation signal differently dependent on a plurality of power ranges, by keeping the parameter within a predetermined stimulation range.

The present invention concerns an apparatus and a method for treatingneurological disorders. In greater detail, the present inventionconcerns an apparatus and a method for treating neurological disordersbased on the feedback of deep brain stimulation, therefore capable ofdetecting biopotentials from a stimulation electrode or fromneighbouring electrodes, correlating such signals with the clinicalstate of the patient and feeding the stimulation parameters back inorder to optimise the therapy.

In the present description and in the subsequent claims, the expression“local biopotentials” means the electric potentials produced by groupsof neurones close to the recording and stimulation electrodes.

In the present description and in the subsequent claims, the expression“local field potentials” means the sum of the pre and post synapticactivity around a stimulation electrode implanted in the brain.

In the present description and in the subsequent claims, the expression“base clinical state” of a patient means the state of the patient in theabsence of therapies, both pharmacological and by stimulation, for asufficiently long time period, so that the effects of the therapies havetotally worn off, in general equal to at least 12 hours.

As known, deep brain stimulation, also known by the acronym DBS, is atherapeutic method based on the modulation of the activities ofstructures of the central nervous system through an electric stimulationdelivered locally. For this purpose, electrodes are implanted byneurosurgery. Electric stimulation consists of delivering a train ofelectric pulses in the brain area of interest through the implantedelectrode, which for this purpose is connected to a pulse generator.

Deep brain stimulation is currently used in clinical trials or for thetreatment of epilepsy, migraines, some psychiatric disturbances, painand movement disorders, such as dystonia, tremor and Parkinson'sdisease. Such a method allows the functional autonomy of patients to beimproved, thus offering an improved quality of life. Since the use ofdeep brain stimulation is particularly consolidated in the treatment ofParkinson's disease, in the present description reference will mainly bemade, although only as an example and not for limiting purposes, to sucha disease. In the case of Parkinson's disease, the implantation areas ofthe electrode most used in clinical practice are some structures of thegrey nucleus, including in particular the internal globus pallidus andthe subthalamic nucleus, as well as the inner peduncle pontine nucleus.The choice of the implantation area is at the discretion of theneurologist based on the symptoms to be tackled. As an example, itshould be considered, indeed, that Parkinson's disease is characterisedby a wide spectrum of motor and non-motor symptoms, where the motorsymptoms comprise, amongst other things, rigidity, bradykinesia, resttremor, akinesia, postural instability, inability to walk and so on.Clinical studies widely support the benefits brought by deep brainstimulation at the subthalamic nucleus, which is therefore the preferredimplantation area in most treatments. Such a treatment method can causevarious side effects including dyskinesia, language and psychiatricdifficulties that can, nevertheless, be mitigated through areprogramming of the stimulation parameters. In the case of conventionalbrain stimulation, the parameter setting process is carried outempirically, requiring time, clinical experience and numerous visits toadjust to the optimal values. Moreover, such adjustment leads to settingthat, even if initially optimal, is unable to adapt to variations thatcame afterwards. Indeed, once the parameters have been set, thestimulation is delivered independently from the clinical state of thepatient, not being able to adapt to possible variations of such aclinical state. Therefore, clinical fluctuations characterising anadvanced stage of Parkinson's disease remain uncontrolled.

In order to overcome the limitations described above, an apparatus fortreating neurological disorders has been made that is capable ofmonitoring the clinical state of the patient by recording aphysiological marker, also known as biomarker, as control variable, andof adapting the stimulation parameters to the clinical state detected.Such a system is known as adaptive brain stimulation. An example of suchan apparatus is described in European patent EP 1 940 508. Through suchan apparatus it is possible to decrease the time necessary to set theoptimal parameters and decrease the occurrence of side effects.

From EP 1 940 508 it is known to use the local field potentials as amarker based on which to adapt the stimulation parameters. The localfield potentials prove particularly suitable for the purpose, since theycorrelate with both motor and non-motor symptoms, they can be recordedby the stimulation electrode even during the stimulation itself, theycan be influenced through stimulation and maintain such properties for along time after the electrode has been implanted.

Neurophysiological recordings carried out through an electrode for deepbrain stimulation have, indeed, shown that the local field potentialsare correlated to the clinical state of the patient, for example to theperformance of movements, as well as to cognitive and behaviouralstimuli. In relation to the correlation between the local fieldpotentials and the symptoms of the disorders to be treated, theApplicant has observed that a lot of the information content of thelocal field potentials relative to the disorders to be treated can beextrapolated through frequency analysis. In other words, the Applicanthas found that there is a link between the power of the local fieldpotentials in certain frequency bands and specific symptoms of thedisturbance to be treated. Specifically, the Applicant has identified arelationship between sets of power values of the local field potentialsand the variations in the clinical state in terms of symptoms to betreated. In particular, the significant oscillatory rhythms in terms oftheir correlation with the symptomatic state of the patient are: lowfrequencies (4-10 Hz), the beta band (alpha/low beta: 11-20 Hz, highbeta: 20-35 Hz), the gamma band (60-80 Hz) and high frequencies (250-350Hz).

In line with such an observation, patent EP 2 004 036 also describes amedical device that, for the treatment of a motor disorder, uses aphysiological marker of the clinical state of a patient. In particular,the physiological marker is calculated based on two valuesrepresentative of the amount of oscillatory activity of thephysiological signal detected, each relative to a different range offrequencies. Patent EP 2 004 036 also refers to the possibility ofadjusting the therapy in feedback based on the two values representativeof the amount of oscillatory activity, in particular by adjusting thestimulation parameters so as to keep the biomarker calculated based onsuch two values, in a predetermined range. EP 2 004 036 does not,however, provide any indication concerning the adjustment logic for anoptimal adaptation of the stimulation parameters.

Also known is the study of Santaniello et al. Described in the articletitled “Closed-Loop Control of Deep Brain Stimulation: A SimulationStudy” published in IEEE Transactions on neural systems andrehabilitation engineering, Vol. 19, No. 1, February 2011, pages 15-24,which has the purpose of developing a closed-loop control system forautomatically adjusting the stimulation parameters based on the neuronalsignals recorded through the same stimulation electrode, in particularbased on the local field potentials. Such a control system comprises,downstream of the transfer function, a saturating trend function thatlimits the amplitude of the stimulation parameters if the transferfunction determines an output value outside a predetermined range. Sucha limitation is therefore carried out as a function of the output of thetransfer function.

However, such a system is unable to correlate the power of the localfield potentials calculated in specific frequency bands with thestimulation parameters, so as to take into account the link observed bythe Applicant between the particular sets of band power values and thespecific symptoms of the disturbance to be treated. In other words, thetransfer function of the control system described in Santaniello appliesthe same law of variability independently from the set to which thepower value that it receives in input belongs.

In light of the above, the Applicant has found the need to devise anapparatus and a method capable of administering a deep brain stimulationtherapy in an optimised manner as a function of the instantaneousclinical state of the patient, expressed through a physiological markercalculated from the local field potentials measured on the patient.

The problem forming the basis of the present invention is therefore thatof making an apparatus and a method for treating neurological disordersthat is able to adapt the stimulation administered in an optimal manneras a function of the instantaneous clinical state of the patient,operating automatically and continuously.

For this purpose, the Applicant has perceived the need to identify a lawof variability that correlates the stimulation parameters with the localfield potentials, based on which it is possible to construct anautomatic control of the therapy that adapts in an optimised and quickmanner to possible changes in the clinical state of the patient.

In accordance with a first aspect thereof, the invention concerns anapparatus for treating neurological disorders comprising

-   -   at least one electrode implantable in the brain of a patient and    -   a processing and stimulation device connected to the at least        one electrode, wherein the processing and stimulation device        comprises    -   at least one stimulation module adapted to generate a        stimulation signal to be sent to the at least one electrode, the        stimulation signal being characterised by a plurality of        parameters,    -   at least one acquisition module of a signal characteristic of        cerebral activity coming from the brain of the patient, adapted        to determine its power in at least one frequency band, and    -   at least one control module of at least one parameter of the        stimulation signal as a function of the power of the acquired        signal characteristic of cerebral activity based on a transfer        function having a saturating trend, wherein the transfer        function is such as to set said at least one parameter (V_(a),        V_(d), V_(f)) of the stimulation signal (V_(stim)) differently        dependent on a plurality of power ranges, keeping it within a        predetermined stimulation range ([V_(i) _(_) _(HighThreshold);        V_(i) _(_) _(LowThreshold)]) with i=a, d, f. In the present        description and in the subsequent claims, the expression        “transfer function having a saturating trend” means a function        that for input values greater than or less than respective first        and second predetermined input values respectively places the        output variable (different from the input variable) equal to a        first and a second predetermined output value and for input        values comprised between the first and the second predetermined        input values, the output can take values based on a        predetermined law of variability. Therefore, in the present        description and in the subsequent claims, the definition of        “saturating trend function” should not be taken in the narrow        sense as a function that forces the input variable to not take        values in output greater or less than predetermined thresholds.

The Applicant has observed that, for example, the oscillations in thebeta band are suppressed following administration of a suitable drug(for example dopamine) and correlate with the preparation andperformance of the movement. Such oscillations reflect the response ofthe grey nucleus to the drug and correlate with the motor state. In thesame way, it has been demonstrated that a deep brain stimulationtreatment induces a power reduction in the beta band.

In other words, when an improvement of the motor state of the patient isobserved after the administration of the drug or after a deep brainstimulation therapy, a corresponding percentage reduction of the powerof the local field potentials calculated in the beta band with respectto the base clinical state, i.e. the clinical state prior to theadministration of therapies, is observed. The variation of the motorstate of the patient is expressed in UPDRS (Unified Parkinson's Diseaserating scale) as percentage values with respect to the base state.

Similarly, the Applicant has observed that the oscillations in the bandof low frequencies (4-10 Hz) increases with a deep brain stimulationand/or pharmacological treatment. In other words, when a percentagedecrease in the UPDRS scale is observed, i.e. an improvement in theclinical state of the patient after administration of the drug or thedeep stimulation therapy, a corresponding increase in the power of thelocal field potentials calculated in the band of low frequencies withrespect to the base clinical state is observed.

The Applicant therefore started from the assumption that an improvementin the clinical state of the patient is correlated to a percentagevariation of the power of the local field potentials, and hypothesised aproportional relationship between such a power calculated in a certainfrequency band, whether it is calculated in the frequency domain, or inthe time domain, and the clinical state, for example expressed in UPDRSscale.

The Applicant has also hypothesised that the relationship betweenstimulation and local field potentials can be expressed through aproportional relationship between the stimulation signal and the powerof the local field potentials. From such an assumption, it follows thatthe clinical state can be expressed as a function of the stimulationsignal.

In accordance with the assumptions outlined above it is possible tocontrol the clinical state of the patient by modifying the stimulationparameters as a function of the power in a certain frequency bandaccording to the mathematical function indicated above.

Such a function determines that, for certain ranges of input powervalues, the stimulation parameters can vary as a function of the inputpower, adapting to the instantaneous clinical state of the patient andfor other ranges of input power values the stimulation parameters areset equal to respective saturation values at which the stimulation wasstill actually effective. In this way, the occurrence of side effectsdue to stimulation therapy is avoided, at the same time ensuring adefinite benefit induced by the stimulation.

Similarly, in accordance with a second aspect thereof, the inventionconcerns a method for treating neurological disorders comprising thesteps consisting of:

-   -   sending at least one stimulation signal characterised by a        plurality of parameters to at least one electrode implantable in        the brain of a patient;    -   acquiring at least one signal characteristic of cerebral        activity coming from the brain of the patient and determining        its power in at least one frequency band; and    -   adjusting at least one parameter of the stimulation signal as a        function of the power of the acquired signal characteristic of        cerebral activity based on a transfer function having a        saturating trend, wherein the transfer function is such as to        set said at least one parameter (V_(a), V_(d), V_(f)) of the        stimulation signal (V_(stim)) differently dependent on a        plurality of power ranges, keeping it within a predetermined        stimulation range ([V_(i) _(_) _(HighThreshold);V_(i) _(_)        _(LowThreshold)]) with i=a, d, f.

Advantageously, the method for treating neurological disorders accordingto the invention achieves the technical effects described above inrelation to the apparatus.

The present invention, in at least one of the aforementioned aspects,can have at least one of the following preferred characteristics, whichare in particular able to be combined with each other as desired inorder to satisfy specific application requirements.

Preferably, the transfer function having a saturating trend as afunction of a plurality of power ranges is a piecewise function, placingthe stimulation parameter equal to a first value of the stimulationparameter for powers of the acquired signal greater than a first powerlimit value and placing the stimulation parameter equal to a secondvalue of the stimulation parameter for powers of the acquired signalbelow a second power limit value according to the following law ofvariability:

${{sat}\left( {U\left( P_{BF} \right)} \right)} = \left\{ \begin{matrix}V_{i\; 2} & {{{per}\mspace{14mu} P_{BF}} \geq P_{{BF}\; 2}} \\{U_{i}\left( P_{BF} \right)} & {{{per}\mspace{14mu} P_{{BF}\; 2}} > P_{BF} > P_{{BF}\; 1}} \\V_{i\; 1} & {{{per}\mspace{14mu} P_{BF}} \leq P_{{BF}\; 1}}\end{matrix} \right.$

with V_(i1) and V_(i2) alternatively respectively placed equal to theminimum value V_(i) _(_) _(LowThreshold) and to the maximum value V_(i)_(_) _(HighThreshold), P_(BF2) and P_(BF1) equal, respectively, to amaximum limit value and a minimum limit value of the saturation rangesof the stimulation parameter V_(i) and U_(i)(P_(BF)) being a law ofvariability U_(i)(P_(BF)) of the stimulation parameter V_(i) outside ofthe saturation ranges. More preferably, the law of variabilityU_(i)(P_(BF)) of the stimulation parameter outside of the saturationranges is of the following type:

${U_{i}\left( P_{BF} \right)} = {{K_{1i}\frac{V_{i\; 2} - V_{i\; 1}}{P_{{BF}\; 2} - P_{{BF}\; 1}}\left( {P_{BF} - P_{{BF}\; 1}} \right)} + {V_{i\; 1}.}}$

Even more preferably, the law of variability U_(i)(P_(BF)) of thestimulation parameter V_(i) outside of the saturation ranges comprises afurther additional term (K_(2i)), thereby resulting in:

${U_{i}\left( P_{BF} \right)} = {{K_{1i}\frac{V_{i\; 2} - V_{i\; 1}}{P_{{BF}\; 2} - P_{{BF}\; 1}}\left( {P_{BF} - P_{{BF}\; 1}} \right)} + V_{i\; 1} + {K_{2i}.}}$

Alternatively, the law of variability U_(i)(P_(BF)) of the stimulationparameter outside of the saturation ranges is of the following type:

${U_{i}\left( P_{BF} \right)} = {{{K_{1i}\left( {V_{i\; 2} - V_{i\; 1}} \right)}*\left( \frac{1}{1 + e^{- {p({P_{BF} - \frac{P_{{BF}\; 2} - P_{{BF}\; 1}}{2}})}}} \right)} + {V_{i\; 1}.}}$

More preferably, the law of variability U_(i)(P_(BF)) of the stimulationparameter V_(i) outside of the saturation ranges comprises a furtheradditional term (K_(2i)), thereby resulting in:

${U_{i}\left( P_{BF} \right)} = {{{K_{1i}\left( {V_{i\; 2} - V_{i\; 1}} \right)}*\left( \frac{1}{1 + e^{- {p({P_{BF} - \frac{P_{{BF}\; 2} - P_{{BF}\; 1}}{2}})}}} \right)} + V_{i\; 1} + {K_{2i}.}}$

Advantageously, the selected laws of variability in feedback allow avast range of adjustment strategies to be carried out through a suitablecalibration of the parameters thereof. This flexibility is an essentialrequirement that allows the use of the apparatus according to thepresent invention in association with multiple different neurologicaldisorders, each characterised by mutually heterogeneous symptoms that inturn correlate with the local field potentials in different frequencybands and with different time dynamics.

Preferably, the at least one acquisition module comprises processingmeans for transforming the acquired signal characteristic of cerebralactivity in the frequency domain.

In an even more preferred manner, the processing means for transformingthe acquired signal characteristic of cerebral activity in the frequencydomain implement a Fourier transform, preferably of the FFT (FastFourier Transform) type. More preferably, the processing means fortransforming the acquired signal characteristic of cerebral activity inthe frequency domain are of the hardware or software type.

Preferably, the at least one acquisition module comprises an integralblock for conditioning the acquired signal characteristic of cerebralactivity.

Alternatively or in combination, the at least one acquisition modulecomprises a derivative block for conditioning the acquired signalcharacteristic of cerebral activity.

In this way, advantageously, it is possible to carry out priorconditioning of the signal fed to the control module that is independentand specific for each stimulation parameter.

Preferably, the at least one stimulation module is a pulse generator.

Preferably, the at least one control module is suitable for implementingthe above law of variability U_(i)(P_(BF)).

Preferably, the frequency band BF and the parameters of the law ofvariability, such as a first V_(i1) and a second V_(i2) threshold valueof a stimulation parameter V_(i), a maximum power value P_(BF2) and aminimum power value P_(BF1) are obtained according to the followingsteps:

a) Identifying at least one maximum threshold value V_(i) _(_)_(HighThreshold) of a stimulation parameter V_(i) above which thepatient shows signs of side effects caused by the stimulation and aminimum threshold value V_(i) _(_) _(LowThreshold) for which the patientshows the minimum or zero benefit induced by stimulation, and placingthe extremes of the predetermined stimulation range ([V_(i2);V_(i1)])alternatively respectively equal to the maximum threshold value V_(i)_(_) _(HighThreshold) and minimum threshold value V_(i) _(_)_(LowThreshold) of the stimulation parameter or to a percentage thereof;

b) Determining the frequency band BF, detecting a frequency peak of thepower spectrum of a signal characteristic of cerebral activity of thepatient recorded in the absence of stimulation, the frequency band BFbeing centred on such a frequency peak and having a bandwidth selectedarbitrarily;

c) Recording the trend over time of the power P_(BF) of a signalcharacteristic of cerebral activity calculated in the frequency band BFin the three conditions:

-   -   base state;    -   active stimulation at the maximum threshold value V₁ _(_)        _(HighThreshold) of the stimulation parameter V_(i) and        pharmacological therapy absent; and    -   active stimulation at the maximum threshold value V_(i) _(_)        _(HighThreshold) of the stimulation parameter V_(i) and        pharmacological therapy administered and active;

d) Identifying a maximum power value P_(BF2) and a minimum power valueP_(BF1) of the trend recorded at step c).

Preferably, the stimulation signal comprises a train of pulses and thestimulation parameter Vi is chosen from the group consisting of:

-   -   The amplitude of the stimulation pulses;    -   The stimulation pulse repetition frequency;    -   The stimulation pulse duration.

Preferably, the maximum power value P_(BF2) of the signal characteristicof cerebral activity calculated in the frequency band BF corresponds tothe power value P_(OFFOFF) that can be determined when the patient is inthe base state and the minimum power value P_(BF1) corresponds to thepower value P_(ONON) that can be determined when the patient issubjected both to pharmacological therapy and to stimulation therapyactive at the maximum threshold value V_(i) _(_) _(HighThreshold) of thestimulation parameter.

More preferably, the frequency band BF is a sub-band of the beta band(10-35 Hz).

Alternatively, the minimum power value P_(BF1) of the signalcharacteristic of cerebral activity calculated in the frequency band BFcorresponds to the power value P_(OFFOFF) that can be determined whenthe patient is in the base state and the maximum power value P_(BF2)corresponds to the power value P_(ONON) that can be determined when thepatient is subjected both to pharmacological therapy and to stimulationtherapy active at the maximum threshold stimulation parameter V_(i) _(_)_(HighThreshold). Preferably, in this case, the frequency band BF is asub-band of the low frequencies (4-10 Hz). Preferably, the signalcharacteristic of cerebral activity is a signal coming from the greynucleus. Preferably, the power calculated in at least one frequency bandof the acquired signal characteristic of cerebral activity is comparedwith a reference value and, based on the difference between thecalculated power and the reference value, a control signal for astimulation module is generated that sets the stimulation parameters.

Preferably, the power P_(BF) of the acquired signal characteristic ofcerebral activity is integrated with a time constant τ.

Advantageously, the time constant τ is selected as a function of theadjustment that is wished to be obtained: the greater the time constantτ, the greater the accuracy of the adjustment but also the delay inresponse of the system. Therefore, the time constant τ with which thepower of band P_(BF) is integrated is chosen seeking the idealcompromise between accuracy and speed of response of the adjustment.

Alternatively or in addition, the power P of the acquired signalcharacteristic of cerebral activity is a derivative.

Further characteristics and advantages of the present invention willbecome clearer from the following detailed description of some preferredembodiments thereof, made with reference to the attached drawings.

The different characteristics in the single configurations can becombined with each other as desired according to the previousdescription, if it were necessary to have advantages resultingspecifically from a particular combination.

In such drawings,

FIG. 1 is a schematic representation of an apparatus for treatingneurological disorders according to a preferred embodiment of thepresent invention;

FIG. 2 is a block diagram of the main steps of the method for treatingneurological disorders in accordance with the present invention;

FIG. 3 is a detailed block diagram of a step of the method for treatingneurological disorders according to the present invention;

FIG. 4a is a diagram of the variation in power in beta band during thecalibration step of the maximum and minimum spectral power thresholds inthe case of Parkinson's disease;

FIG. 4b is a diagram of the variation in spectral power at the lowfrequencies during the calibration step of the maximum and minimumspectral power thresholds in the case of Parkinson's disease.

In the following description, to illustrate the figures identicalreference numerals or symbols are used to indicate constructive elementswith the same function. Moreover, for the sake of clarity ofillustration, some references are not repeated in all of the figures.

With reference to FIG. 1, an apparatus for treating neurologicaldisorders is shown, wholly indicated with 10.

The apparatus for treating neurological disorders 10 comprises at leastone electro-catheter 11 suitable for being implanted in the brain of apatient to administer an electric stimulation. The electro-catheter 11preferably comprises at least three metallic contacts accessible throughexternal connections also called electrodes 12. However, it is obviouslypossible to hypothesise alternative solutions in which the electrodesare not necessarily carried by one same electro-catheter.

The electrodes 12 are connected to a processing and stimulation device14 that, in the embodiment illustrated in FIG. 1, comprises threefunctional modules connected together in feedback and interoperating: astimulation module 16, an acquisition module 18 and a control module 20.

The stimulation module 16 is adapted to generate a stimulation signalV_(stim) characterised by a set of parameters V_(a), V_(d), V_(f), andto send to the electrodes 12 the stimulation signal generated. Inparticular, the stimulation module 16 is a generator of pulses definedby the amplitude, frequency and duration of the pulses.

The acquisition module 18 is assigned to the acquisition of a signalcharacteristic of cerebral activity coming from the brain of thepatient. In detail, the acquisition module 18 comprises processing meansfor transforming the acquired signal characteristic of cerebral activityin the frequency domain. Specifically, the processing means carry out anFFT (Fast Fourier Transform) and can be made through hardware meansand/or software means. The acquisition module 18 also preferablycomprises an integral block and a derivative block (not illustrated) ofthe signal characteristic of cerebral activity transformed in thefrequency domain.

The control module 20 implements an adjuster, preferably a feedbackcontroller. As illustrated more clearly in FIG. 3, the control module 20is functionally connected, upstream, to the acquisition module 18 and,downstream, to the stimulation module 16 that determines the stimulationsignal V_(stim). As a function of the spectral power of the signalcharacteristic of cerebral activity acquired by the acquisition module18, the control module 20 determines at least one signal based on whichat least one parameter V_(a), V_(d), V_(f) of the stimulation signalV_(stim) set by the stimulation module 16 is defined.

Advantageously, the control module 20 receives in input the signalacquired in the time domain or transformed in the frequency domain bythe acquisition module 18 to determine its power. Based on such a power,preferably integrated based on a time constant τ and/or derivedaccording to specificities of the stimulation parameter to be adjusted,the stimulation parameters are calculated based on a transfer functionhaving a saturating trend such as to also determine that the stimulationparameters are variable between two saturation values (V_(i) _(_)_(HighThreshold); V_(i) _(_) _(LowThreshold)) between which thestimulation is actually effective.

In particular, the transfer function having a saturating trend isimplemented as a piecewise function based on ranges of values of theinput power, i.e. such as to place the stimulation parameter V_(i) equalto a maximum value V_(i) _(_) _(HighThreshold) or to a minimum valueV_(i) _(_) _(LowThreshold) in the saturation ranges, allowing thestimulation parameter V_(i) to vary, outside the saturation ranges, as afunction of the power P_(BF) of the signal acquired according to a lawof variability U_(i)(P_(BF)).

This translates into the following transfer function, where thesaturation ranges correspond to powers P_(BF) of the acquired signalgreater than a first power limit value P_(BF2) or powers P_(BF) of theacquired signal below a second power limit value P_(BF1):

${{sat}\left( {U\left( P_{BF} \right)} \right)} = \left\{ {\begin{matrix}V_{i\; 2} & {{{per}\mspace{14mu} P_{BF}} \geq P_{{BF}\; 2}} \\{U_{i}\left( P_{BF} \right)} & {{{per}\mspace{14mu} P_{{BF}\; 2}} > P_{BF} > P_{{BF}\; 1}} \\V_{i\; 1} & {{{per}\mspace{14mu} P_{BF}} \leq P_{{BF}\; 1}}\end{matrix}.} \right.$

In particular, the law of variability U_(i)(P_(BF)) of the stimulationparameter outside the saturation ranges is of the following type:

${U_{i}\left( P_{BF} \right)} = {{K_{1i}\frac{V_{i\; 2} - V_{i\; 1}}{P_{{BF}\; 2} - P_{{BF}\; 1}}\left( {P_{BF} - P_{{BF}\; 1}} \right)} + V_{i\; 1} + {K_{2i}.}}$

Alternatively, the law of variability U_(i)(P_(BF)) of the stimulationparameter outside of the saturation ranges is of the sigmoid type:

${U_{i}\left( P_{BF} \right)} = {{{K_{1i}\left( {V_{i\; 2} - V_{i\; 1}} \right)}*\left( \frac{1}{1 + e^{- {p({P_{BF} - \frac{P_{{BF}\; 2} - P_{{BF}\; 1}}{2}})}}} \right)} + V_{i\; 1} + {K_{2i}.}}$

In both cases, the parameter K_(1i) represents a proportional adjustmentfactor preferably having unitary value so that the maximum excursion ofP_(BF) corresponds to the maximum excursion of the output V_(i)(P_(BF)).In the case in which the parameter K_(1i) takes on values greater than1, an additional saturation block is foreseen in order to ensure thatthe stimulation parameter V_(i) is kept within the predeterminedstimulation range. In the sole case of sigmoid function, the parameter pis adjusted based on the desired value of the function U_(i)(P_(BF))around the point P_(BF2) and P_(BF1).

Specifically, since deep brain stimulation uses a stimulus defined bythree stimulation parameters V_(a), V_(d), V_(f) relative, respectively,to amplitude, duration and frequency of the stimulation signal V_(stim),the control module 20 foresees to implement a respective law ofvariability V_(a)(P_(BF)),V_(d)(P_(BF)),V_(f)(P_(BF)) for eachstimulation parameter V_(a), V_(d), V_(f). The stimulation signalV_(stim) in output from the stimulation module 16 is characterised bythe parameters V_(a), V_(d), V_(f), calculated based on the respectiveoutput of the control module 20.

Advantageously, the time constant τ based on which the integration ofthe spectral power P_(BF) takes place, is selected as a function of thecontrol requirements: the greater the time constant τ the smaller thevariance on the evaluation of the spectral power P_(BF) of the acquiredsignal and therefore on the instantaneous clinical state of the patient.However, increasing the time constant τ increases the delay inidentifying the clinical state of the patient.

Preferably, the control allows variable setting of the time constant τ,so that the most suitable time constant can be set each time based onthe specific application, taking into account the compromise betweenspeed and accuracy of detection of the power.

The adjuster implemented by the control module 20 is characterised by awide degree of flexibility thanks to the possibility of calibrating theadjustment parameters K_(1i), K_(2i) P_(BF2), P_(BF1), τ, V_(i1),V_(i2). It is thus possible to carry out a vast range of adjustmentstrategies.

The operating method 100 of the apparatus for treating neurologicaldisorders 10 is schematically illustrated in FIG. 2.

Prior to the stimulation treatment there is an initialisation session(step 110). The initialisation session is carried out after the patienthas spent a sufficient time (generally 12 hours) without pharmacologicalmedication. After such a time period without pharmacological therapy,the patient is considered to be in the so-called “OFF-OFF” or baseclinical condition, i.e. in the absence of stimulation and with effectof pharmacological therapy having worn off.

Then there is the identification (step 111) of at least one of thethreshold values of the specific stimulation parameters of the patientbased on which to set the treatment. In particular, in simplifyingterms, the amplitude of the stimulation voltage is identified.

Such identification takes place through an expert, like for example aneurologist specialised in the treatment of neurological disordersthrough deep brain stimulation. The step of identifying the parameters(step 111) therefore takes place through a series of stimulation testswith different parameter values, based on which the expert decides themaximum threshold value V_(i) _(_) _(HighThreshold), to obtain themaximum clinical effect before the appearance of side effects, andminimum threshold value V_(i) _(_) _(LowThreshold), to obtain theminimum or zero clinical effect. The saturation values of thestimulation parameters V_(i2) and V_(i1) can be placed equal,respectively, to the maximum threshold value V_(i) _(_) _(HighThreshold)and minimum threshold value V_(i) _(_) _(LowThreshold) or alternatively,respectively equal to the minimum threshold value V_(i) _(_)_(LowThreshold) and maximum threshold value V_(i) _(_) _(HighThreshold).

In the case in which the parameter analysed is the amplitude V_(a) ofthe stimulation signal V_(stim), the step of identifying the stimulationparameters leads to determining the maximum and minimum amplitude of thevoltage that can be set V_(a) _(_) _(HighThreshold) and V_(a) _(_)_(LowThreshold). Similarly, the maximum/minimum frequency and/or themaximum/minimum duration of the stimulation signal V_(stim) can beidentified.

Then there is a recording (step 112) of the neurophysiological signal:the harmonic content of the neurophysiological signal of the specificpatient in the absence of stimulation is detected and analysed toidentify the characteristics of the specific frequency spectrum of thepatient. In particular, at least one frequency peak is identified, withrespect to which the at least one frequency band BF is centred based onwhich to calculate the spectral power of the signal. The frequency bandsare defined through a minimum frequency and a maximum frequency:fw_min<BF<fw_max and correspond to the frequency bands with which thesymptoms of the neurological disorders that it is wished to counteractmost probably correlate. The frequencies fw_min and fw_max can beselected arbitrarily.

Once the stimulation parameters and the frequency band have beendefined, there is a calibration step (step 113) in which the signalcharacteristic of cerebral activity is recorded in a plurality ofdifferent conditions to extract the values of the power in the frequencyband defined previously. Specifically, for the calibration step (step113), the neurophysiological signal of the patient at the base state isdetected, i.e. in the absence of therapies of any kind (pharmacologicalor stimulation) also called OFF-OFF state, and the power in the band ofinterest is stored. The recording of the neurophysiological signal atthe OFF-OFF state takes place for an initial period, in general equal to20 minutes. Once the initial period has ended, the stimulation isbrought to the maximum threshold stimulation values V_(i) _(_)_(HighThreshold) determined previously. The processing and stimulationdevice proceeds to store the power of the signal characteristic ofcerebral activity of the patient in the clinical OFF-ON state, i.e. inthe absence of pharmacological therapy (LEVOdopamine), but in thepresence of stimulation. After a further time period, in general equalto another 20 minutes, the pharmacological therapy is started againproceeding to store the power. After a third time period, the drug takenis considered to be completely assimilated and the patient is in theclinical ON-ON state, i.e. in the presence of pharmacological therapyand of stimulation. The storage of the power of the signalcharacteristic of cerebral activity of the patient is therefore ended.

Once the storage has ended, in the three initialisation steps 110, ofthe power calculated in the frequency band identified initially, themaximum power value P_(BF2) and minimum power value P_(BF1) areextrapolated.

In the specific case illustrated in FIG. 4a , relative to a frequencyband of interest coinciding with a sub-band of the beta band (10-35 Hz),the maximum power value P_(BF2) coincides with the power value in theOFF-OFF state (P_(βOFFOFF)), whereas the minimum power value P_(BF1)coincides with the power value in the ON-ON state (P_(βONON)).

In example terms, the case is also shown in which the frequency band ofinterest coincides with the low frequencies (4-10 Hz). In this case, asshown in FIG. 4b , the minimum power value P_(BF1) coincides with thepower value in the OFF-OFF state (P_(lowOFFOFF)) whereas the maximumpower value P_(BF2) coincides with the power value at the ON-ON state(P_(lowONON)).

Once the initialisation step 110 of the therapy has ended, the method100 for treating neurological disorders comprises the repetition of thefollowing steps.

The delivery of the deep brain stimulation is started (step 120).

Thereafter (step 130), the acquisition module 18 records a signalcharacteristic of cerebral activity of the patient (sub-step 131),preferably the local field potentials LFP recorded at the grey nucleus,and thereafter transforms it (sub-step 132) preferably in the frequencydomain, for example through FFT (Fast Fourier Transform), determiningits spectral power P_(BF) (sub-step 133). Preferably, the power is alsointegrated based on the time constant τ (sub-step 134).

Finally, based on the spectral power P_(BF) recorded, there is a step ofupdating the stimulation parameters (step 140).

For this purpose, the control module 20 preferably compares the powerP_(BF) with a range of reference values [P_(BF2); P_(BF1)] thatcorrelate more with the frequency band of interest. Based on thedifference between the power P_(BF) calculated and the lower limitP_(BF1) of such a reference range [P_(BF2); P_(BF1)] a control signalfor a stimulation module (16) is generated which sets the stimulationparameters (V_(a), V_(d), V_(f)) according to the law of variabilityV_(i)(P_(BF)) given above.

In the case in which the frequency band of interest coincides with asub-band of the beta band (10-35 Hz) that, as will be seen hereinafter,proves particularly suitable for the treatment of some symptoms ofParkinson's disease, the upper extreme P_(BF2) of the range of values isequal to the power P_(βOFFOFF) at the OFF-OFF state and the lowerextreme P_(BF1) of the range of values is equal to the power P_(βONON)at the ON-ON state determined in the initialisation step, withP_(BF)2>P_(BF1).

In example terms, the case is now discussed in which the treatmentmethod according to the invention is specifically used for treatingclinical-motor functions of Parkinson's disease that most correlate withthe beta band β, which has therefore been identified as the referencefrequency band BF based on which to calculate the spectral power of theacquired local field potentials. For this treatment it has also provensufficient to carry out an adaptation of just the stimulation amplitudeV_(a).

In this case, the law of variability takes the form:

${U_{i}\left( P_{BF} \right)} = {{K_{1i}\frac{V_{i\; 2} - V_{i\; 1}}{P_{{BF}\; 2} - P_{{BF}\; 1}}\left( {P_{BF} - P_{{BF}\; 1}} \right)} + V_{i\; 1} + K_{2i}}$

With the adjustment parameters K_(1i), P_(BF2), P_(BF1), V_(i1), V_(i2),K_(2i) equal to:

P_(BF)=P_(β);

P_(BF2)=P_(βOFFOFF)

P_(BF1)=P_(βONON)

V_(i2)=V_(a) _(_) _(HighThreshold)

V_(i1)=V_(a) _(_) _(LowThreshold)

K_(1i)=K_(a)=1

K_(2i)=0

In the case of the treatment of the symptoms of Parkinson's disease thatcorrelate with the beta band, there is therefore a simplified adjustmentmodel based on the following law of variability:

${V_{a}\left( P_{\beta} \right)} = {{{sat}\left( P_{\beta} \right)} = \left\{ \begin{matrix}V_{a\_ HighThreshold} & {{{per}\mspace{14mu} P_{\beta}} \geq P_{\beta \; {OFFOFF}}} \\{\frac{\begin{matrix}{V_{a\_ HighThreshold} -} \\V_{a\_ LowThreshold}\end{matrix}}{\begin{matrix}{P_{\beta \; {OFFOFF}} -} \\P_{\beta \; {ONON}}\end{matrix}}\begin{matrix}{\left( {P_{\beta} - P_{\beta \; {ONON}}} \right) +} \\V_{a\_ LowThreshold}\end{matrix}} & \begin{matrix}{{{per}\mspace{14mu} P_{\beta \; {OFFOFF}}} >} \\{P_{\beta} > P_{\beta \; {ONON}}}\end{matrix} \\V_{a\_ LowThreshold} & {{{per}\mspace{14mu} P_{\beta}} \leq P_{\beta \; {ONON}}}\end{matrix} \right.}$

Alternatively, the case is now discussed in which the treatment methodaccording to the invention is specifically used for the treatment of theclinical-motor fluctuations of Parkinson's disease that most correlatewith the band of low frequencies (4-10 Hz), which has therefore beenidentified as reference frequency band BF based on which to calculatethe spectral power of the acquired local field potentials. For thistreatment, it also proved sufficient to carry out an adaptation of justthe stimulation amplitude V_(a).

In this case, the law of variability takes the form

${U_{i}\left( P_{BF} \right)} = {{K_{1i}\frac{V_{{i\; 2} -}V_{i\; 1}}{P_{{BF}\; 2} - P_{{BF}\; 1}}\left( {P_{{BF}\; 2} - P_{BF}} \right)} + V_{i\; 1} + {K_{2i}.}}$

With the adjustment parameters K₁i, P_(BF2), P_(BF1), V_(i1), V_(i2),K_(2i) equal to:

P_(BF)=P_(low)

P_(BF)2=P_(lowONON)

P_(BF1)=P_(lowOFFOFF)

V_(i2)=V_(a) _(_) _(LowThreshold)

V_(i1)=V_(a) _(_) _(HighThreshold)

K_(1i)=K_(a)=1

K_(2i)=0

In the case of treatment of the symptoms of Parkinson's disease thatcorrelate most with the low frequencies, there is therefore a simplifiedadjustment model defined by the following law of variability:

${V_{a}\left( P_{low} \right)} = {{{sat}\mspace{11mu} \left( P_{low} \right)} = \left\{ \begin{matrix}V_{a_{LowThreshold}} & {{{per}\mspace{14mu} P_{low}} \geq P_{lowONON}} \\{\frac{\begin{matrix}{V_{a_{LowThreshold}} -} \\V_{a_{HighThreshold}}\end{matrix}}{\begin{matrix}P_{{lowONON} -} \\P_{lowOFFOFF}\end{matrix}}\begin{matrix}{\left( {P_{low} - P_{lowOFFOFF}} \right) +} \\V_{a_{HighThreshold}}\end{matrix}} & \begin{matrix}{{{per}\mspace{14mu} P_{lowOFFOFF}} >} \\{P_{low} > P_{lowONON}}\end{matrix} \\V_{a_{HighThreshold}} & {{{per}\mspace{14mu} P_{low}} \leq P_{lowOFFOFF}}\end{matrix} \right.}$

From the description that has been made the characteristics of theapparatus and of the method for treating neurological disorders objectof the present invention are clear, just as the relative advantages arealso clear.

From the embodiments described above further variants are possible,without departing from the teaching of the invention.

Finally, it is clear that an apparatus and a method for treatingneurological disorders thus conceived can undergo numerous modificationsand variants, all of which are covered by the invention; moreover, allof the details can be replaced by technically equivalent elements. Inpractice, the materials used, as well as the sizes, can be whateveraccording to the technical requirements.

1. Apparatus (10) for treating neurological disorders comprising atleast one electrode (12) implantable in the brain of a patient and aprocessing and stimulation device (14) connected to the at least oneelectrode (12), wherein the processing and stimulation device (14)comprises at least one stimulation module (16) adapted to generate astimulation signal (V_(stim)) to be sent to the at least one electrode(12), the stimulation signal (V_(stim)) being characterised by aplurality of parameters (V_(a), V_(d), V_(f)), at least one acquisitionmodule (18) of a signal characteristic of cerebral activity coming fromthe brain of the patient adapted to determine its power (P_(BF)) in atleast one frequency band (BF), and at least one control module (20) ofat least one parameter (V_(a), V_(d), V_(f)) of the stimulation signal(V_(stim)) as a function of the power (P_(BF)) of the signalcharacteristic of cerebral activity acquired, based on a transferfunction having a saturating trend, wherein the transfer function issuch as to set said at least one parameter (V_(a), V_(d), V_(f)) of thestimulation signal (V_(stim)) differently dependent on a plurality ofpower ranges, by keeping the at least one parameter (V_(a), V_(d),V_(f)) within a predetermined stimulation range ([V_(i) _(_)_(HighThreshold);V_(i) _(_) _(LowThreshold)]) with i=a, d, f. 2.Apparatus (10) for treating neurological disorders according to claim 1,wherein the transfer function with saturating trend based on a pluralityof power ranges is a piecewise function, placing the stimulationparameter equal to a first value (V_(i2)) of the stimulation parameterfor powers of the signal acquired above a first power limit value andplacing the stimulation parameter equal to a second value (V_(i1)) ofthe stimulation parameter for powers of the signal acquired below asecond power limit value according to the following law:${{sat}\left( {U\left( P_{BF} \right)} \right)} = \left\{ \begin{matrix}V_{i\; 2} & {{{per}\mspace{14mu} P_{BF}} \geq P_{{BF}\; 2}} \\{U_{i}\left( P_{BF} \right)} & {{{per}\mspace{14mu} P_{{BF}\; 2}} > P_{BF} > P_{{BF}\; 1}} \\V_{i\; 1} & {{{per}\mspace{14mu} P_{BF}} \leq P_{{BF}\; 1}}\end{matrix} \right.$ with V_(i1) and V_(i2) alternatively set equal tothe minimum value V_(i) _(_) _(LowThreshold) and to the maximum valueV_(i) _(_) _(HighThreshold) of a stimulation parameter V_(i), P_(BF2)and P_(BF1) equal, respectively, to a maximum limit value and a minimumlimit value of the saturation ranges of the stimulation parameter V_(i)and U_(i)(P_(BF)) being a law of variability U_(i)(P_(BF)) of thestimulation parameter V_(i) outside the saturation ranges.
 3. Apparatus(10) for treating neurological disorders according to claim 2, whereinthe law of variability (U_(i)(P_(BF))) of the stimulation parameter(V_(i)) outside the saturation ranges is of the following type:${U_{i}\left( P_{BF} \right)} = {{K_{1i}\frac{V_{i\; 2} - V_{i\; 1}}{P_{{BF}\; 2} - P_{{BF}\; 1}}\left( {P_{BF} - P_{{BF}\; 1}} \right)} + {V_{i\; 1}.}}$4. Apparatus (10) for treating neurological disorders according to claim3, wherein the law of variability (U_(i)(P_(BF))) of the stimulationparameter (V_(i)) outside the saturation ranges comprises a furtheradditional term (K_(2i)), thereby resulting in:${U_{i}\left( P_{BF} \right)} = {{K_{1i}\frac{V_{i\; 2} - V_{i\; 1}}{P_{{BF}\; 2} - P_{{BF}\; 1}}\left( {P_{BF} - P_{{BF}\; 1}} \right)} + V_{i\; 1} + {K_{2i}.}}$5. Apparatus (10) for treating neurological disorders according to claim2, wherein the law of variability (U_(i)(P_(BF))) of the stimulationparameter (V_(i)) outside of the saturation ranges is of the followingtype:${U_{i}\left( P_{BF} \right)} = {{{K_{i}\left( {V_{i\; 2} - V_{i\; 1}} \right)}*\left( \frac{1}{1 + e^{- {p({P_{BF} - \frac{P_{{BF}\; 2} - P_{{BF}\; 1}}{2}})}}} \right)} + {V_{i\; 1}.}}$6. Apparatus (10) for treating neurological disorders according to claim5, wherein the law of variability (U_(i)(P_(BF))) of the stimulationparameter (V_(i)) outside the saturation ranges comprises a furtheradditional term (K_(2i)), thereby resulting in:${U_{i}\left( P_{BF} \right)} = {{{K_{i}\left( {V_{i\; 2} - V_{i\; 1}} \right)}*\left( \frac{1}{1 + e^{- {p({P_{BF} - \frac{P_{{BF}\; 2} - P_{{BF}\; 1}}{2}})}}} \right)} + V_{i\; 1} + {K_{2i}.}}$7. Apparatus (10) for treating neurological disorders according to anyone of the previous claims, wherein the at least one acquisition module(18) comprises processing means for transforming the acquired signalcharacteristic of cerebral activity in the frequency domain, preferablyof the type implementing a Fast Fourier Transform.
 8. Apparatus (10) fortreating neurological disorders according to any one of the previousclaims, wherein the at least one acquisition module (18) comprises anintegral block and/or a derivative block for signal conditioning of therecorded signal characteristic of cerebral activity.
 9. Apparatus (10)for treating neurological disorders according to any one of the previousclaims, wherein the at least one stimulation module (16) is a pulsegenerator.
 10. Apparatus (10) for treating neurological disordersaccording to claim 9, wherein the pulse generator generates astimulation signal (V_(stim)) comprising a pulse train, wherein at leastone stimulating parameter (V_(a), V_(d), V_(f)) of the plurality ofstimulating parameters (V_(a), V_(d), V_(f)) characterising thestimulation signal (V_(stim)) is chosen from the group consisting of:The amplitude of the stimulation pulses; The stimulation pulserepetition frequency; The stimulation pulse duration.
 11. Apparatus (10)for treating neurological disorders according to any one of the previousclaims, wherein the frequency band (BF) is a sub-band of the beta band(10-35 Hz) or a sub-band of the low frequencies (4-10 Hz).
 12. Method(100) for treating neurological disorders comprising the stepsconsisting of: sending (120) at least one stimulation signal (V_(stim))characterised by a plurality of parameters (V_(a), V_(d), V_(f)) to atleast one electrode (12) implantable in the brain of a patient;acquiring (130) at least one signal characteristic of cerebral activitycoming from the brain of the patient and determining the power (P_(BF))in at least one frequency band (BF); and adjusting (140) at least oneparameter (V_(a), V_(d), V_(f)) of the stimulation signal (V_(stim)) asa function of the power (P_(BF)) of the signal characteristic ofcerebral activity acquired, based on a transfer function having asaturating trend, wherein the transfer function is such as to set saidat least one parameter (V_(a), V_(d), V_(f)) of the stimulation signal(V_(stim)) differently dependent on a plurality of power ranges, bykeeping the at least one parameter (V_(a), V_(d), V_(f)) within apredetermined stimulation range ([V_(i) _(_) _(HighThreshold);V_(i) _(_)_(LowThreshold)]) with i=a, d, f.
 13. Method (100) for treatingneurological disorders according to claim 12, wherein the transferfunction with saturating trend based on a plurality of power ranges is apiecewise function, setting the stimulation parameter equal to a firstvalue (V_(i1)) of the stimulation parameter for powers of the signalacquired above a first power limit value and setting the stimulationparameter equal to a second value (V_(i2)) of the stimulation parameterfor powers of the signal acquired below a second power limit valueaccording to the following law:${{sat}\left( {U\left( P_{BF} \right)} \right)} = \left\{ \begin{matrix}V_{i\; 2} & {{{per}\mspace{14mu} P_{BF}} \geq P_{{BF}\; 2}} \\{U_{i}\left( P_{BF} \right)} & {{{per}\mspace{14mu} P_{{BF}\; 2}} > P_{BF} > P_{{BF}\; 1}} \\V_{i\; 1} & {{{per}\mspace{14mu} P_{BF}} \leq P_{{BF}\; 1}}\end{matrix} \right.$ with V_(i1) and V_(i2) alternatively setrespectively equal to the minimum value V_(i) _(_) _(LowThreshold) andto the maximum value V_(i) _(_) _(HighThreshold) of a stimulationparameter V_(i), P_(BF2) and P_(B1) equal, respectively to a maximumlimit value and a minimum limit value of the saturation ranges of thestimulation parameter V_(i) and U_(i)(P_(BF)) being a law of variabilityU_(i)(P_(BF)) of the stimulation parameter V_(i) outside the saturationranges.
 14. Method (100) for treating neurological disorders accordingto claim 13, wherein the law of variability (U_(i)(P_(BF))) of thestimulation parameter (V_(i)) outside the saturation ranges is of thefollowing type:${U_{i}\left( P_{BF} \right)} = {{K_{i}\frac{V_{i\; 2} - V_{i\; 1}}{P_{{BF}\; 2} - P_{{BF}\; 1}}\left( {P_{BF} - P_{{BF}\; 1}} \right)} + {V_{i\; 1}.}}$15. Method (100) for treating neurological disorders according to claim14, wherein the law of variability (U_(i)(P_(BF))) of the stimulationparameter (V_(i)) outside the saturation ranges comprises a furtheradditional term (K_(2i)), thereby resulting in:${U_{i}\left( P_{BF} \right)} = {{K_{1i}\frac{V_{i\; 2} - V_{i\; 1}}{P_{{BF}\; 2} - P_{{BF}\; 1}}\left( {P_{BF} - P_{{BF}\; 1}} \right)} + V_{i\; 1} + {K_{2i}.}}$16. Method (100) for treating neurological disorders according to claim13, wherein the law of variability (U_(i)(P_(BF))) of the stimulationparameter (V_(i)) outside the saturation ranges is of the followingtype:${U_{i}\left( P_{BF} \right)} = {{{K_{i}\left( {V_{i\; 2} - V_{i\; 1}} \right)}*\left( \frac{1}{1 + e^{- {p({P_{BF} - \frac{P_{{BF}\; 2} - P_{{BF}\; 1}}{2}})}}} \right)} + {V_{i\; 1}.}}$17. Method (100) for treating neurological disorders according to claim16, wherein the law of variability (U_(i)(P_(BF))) of the stimulationparameter (V_(i)) outside the saturation ranges comprises a furtheradditional term (K_(2i)), thereby resulting in:${U_{i}\left( P_{BF} \right)} = {{{K_{i}\left( {V_{i\; 2} - V_{i\; 1}} \right)}*\left( \frac{1}{1 + e^{- {p({P_{BF} - \frac{P_{{BF}\; 2} - P_{{BF}\; 1}}{2}})}}} \right)} + V_{i\; 1} + {K_{2i}.}}$18. Method (100) for treating neurological disorders according to anyone of claims 12 to 17, wherein the stimulation signal (V_(stim))comprises a train of pulses and the stimulation parameter (V_(a), V_(d),V_(f)) is selected from the group consisting of: The amplitude of thestimulation pulses; The stimulation pulse repetition frequency; Thestimulation pulse duration.
 19. Method (100) for treating neurologicaldisorders according to any one of claims 12 to 18, wherein the frequencyband (BF) and the parameters of the law of variability are obtainedaccording to the following steps: a) identifying (111) at least onemaximum threshold value (V_(i) _(_) _(HighThreshold)) of a stimulationparameter (V_(i)) beyond which the patient shows signs of actual sideeffects induced by the stimulation and a minimum threshold value (V_(i)_(_) _(LowThreshold)) for which the patient shows the minimum or zerobenefit induced by stimulation, and setting the extremes of saidpredetermined stimulation range ([V_(i2);V_(i1)]) alternatively andrespectively equal to the threshold values (V_(i) _(_) _(HighThreshold))and (V_(i) _(_) _(LowThreshold)) of the stimulation parameter (V_(i)) orto a percentage thereof; b) determining (112) the frequency band (BF),by detecting a frequency peak of the power spectrum of a signalcharacteristic of cerebral activity of the patient recorded in theabsence of stimulation, the frequency band (BF) being centred on such afrequency peak and having a bandwidth selected arbitrarily; c) recording(113) the variation over time of the spectral power (P_(BF)) of a signalcharacteristic of cerebral activity calculated in the frequency band(BF) in the three conditions: base state; active stimulation at themaximum threshold stimulation parameter (V_(i) _(_) _(HighThreshold))and pharmacological therapy absent; and active stimulation at themaximum threshold stimulation parameter (V_(i) _(_) _(HighThreshold))and pharmacological therapy administered and active; d) identifying(114) a maximum spectral power value (P_(BF2)) and a minimum spectralpower value (P_(BF1)) of the variation recorded in step c).
 20. Method(100) for treating neurological disorders according to claim 19, whereinthe maximum spectral power value (P_(BF2)) of the signal characteristicof cerebral activity calculated in the frequency band (BF) correspondsto a spectral power value (P_(OFFOFF)) able to be determined when thepatient is in the base state and the minimum spectral power value(P_(BF1)) corresponds to a spectral power value (P_(ONON)) able to bedetermined when the patient undergoes both a pharmacological therapy andan active stimulation therapy at the maximum threshold value (V_(i) _(_)_(HighThreshold)) of the stimulation parameter.
 21. Method (100) fortreating neurological disorders according to claim 20, wherein thefrequency band (BF) is a sub-band of the beta band (10-35 Hz). 22.Method (100) for treating neurological disorders according to claim 19,wherein the minimum spectral power (P_(BF1)) of the signalcharacteristic of cerebral activity calculated in the frequency band(BF) corresponds to a spectral power value (P_(OFFOFF)) able to bedetermined when the patient is in the base state and the maximumspectral power value (P_(BF2)) corresponds to the spectral power value(P_(ONON)) able to be determined when the patient undergoes both apharmacological therapy and an active stimulation therapy at the maximumthreshold value (V_(i) _(_) _(HighThreshold)) of the stimulationparameter.
 23. Method (100) for treating neurological disordersaccording to claim 22, wherein the frequency band (BF) is a sub-band ofthe low frequencies (4-10 Hz).